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O-LevelAdditional MathematicsDifferentiation and integration4037/12 · Oct/Nov 2015 · Q87 Marks

Find the equation of the tangent to the curve y = (2x-1) / √(x²+5) at the point where x = 2.

  1. Find the equation of the tangent to the curve y = (2x-1) / √(x²+5) at the point where x = 2.[7]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.

  1. [B1] for (2x)(x²+5)^(-1/2) for a quotient or (2x)(x²+5)^(-3/2) for a product (allow if either seen in separate working)
  2. [M1] for attempt to differentiate a quotient or a correct product
  3. [A1] for all correct, allow unsimplified
  4. [B1, B1] B1 for each (when x=2, y=1 and dy/dx=4/9)
  5. [M1] for attempt at straight line equation, must be tangent using their gradient and y
  6. [A1] allow unsimplified.

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About this question

Topic
Differentiation and integration, O-Level Additional Mathematics (syllabus 4037). Structured question, 7 marks.
Source
O-Level Additional Mathematics, Oct/Nov 2015 Paper 1 Variant 2, question 8.

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